Frequency Transitions in Odor-Evoked Neural Oscillations

Neuron

Article

Frequency Transitions inOdor-Evoked Neural OscillationsIori Ito,1 Maxim Bazhenov,2 Rose Chik-ying Ong,1,3 Baranidharan Raman,1,4 and Mark Stopfer1,*1National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD 20892, USA2Department of Cell Biology and Neuroscience, University of California, Riverside, CA 92521, USA3Department of Biochemistry, The Chinese University of Hong Kong, Hong Kong4Chemical Science and Technology Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Stop 8362,

Gaithersburg, MD 20899-8362, USA

*Correspondence: [email protected]

DOI 10.1016/j.neuron.2009.10.004

SUMMARY

In many species, sensory stimuli elicit the oscillatorysynchronization of groups of neurons. What deter-mines the properties of these oscillations? In theolfactory system of the moth, we found that odorselicited oscillatory synchronization through a neuralmechanism like that described in locust andDrosophila. During responses to long odor pulses,oscillations suddenly slowed as net olfactoryreceptor neuron (ORN) output decreased; thus, stim-ulus intensity appeared to determine oscillation fre-quency. However, changing the concentration ofthe odor had little effect upon oscillatory frequency.Our recordings in vivo and computational modelsbased on these results suggested that the main effectof increasing odor concentration was to recruit addi-tional, less well-tuned ORNs whose firing rates weretightly constrained by adaptation and saturation.Thus, in the periphery, concentration is encodedmainly by the size of the responsive ORN population,and oscillation frequency is set by the adaptationand saturation of this response.

INTRODUCTION

Sensory stimulus-evoked neural oscillations have been de-

scribed in many animals (Adrian, 1942; Bressler and Freeman,

1980; Galambos et al., 1981; Gray et al., 1989; Laurent and

Naraghi, 1994; Stopfer et al., 1997; Schadow et al., 2007; Tanaka

et al., 2009). For a particular modality in a given species, oscilla-

tion frequency often seems unrelated to stimulus intensity. In the

locust olfactory system, for example, odors elicit�20 Hz oscilla-

tions that vary little in frequency even when odor concentration

varies over five orders of magnitude (Stopfer et al., 2003; Assisi

et al., 2007). In some cases, though, stimulus intensity does

appear to modulate oscillation frequency; the changing velocity

of a visual stimulus, for example, can systematically change the

frequency of gamma oscillations in the cat visual cortex (Gray

and Prisco, 1997). What determines the frequencies of these

oscillations?

692 Neuron 64, 692–706, December 10, 2009 ª2009 Elsevier Inc.

Here, we used the insect olfactory system to clarify the encod-

ing of odor intensity and the relationship between stimulus inten-

sity and oscillation frequency. In insects, odor molecules are

first detected by olfactory receptor neurons (ORNs). Axons

from ORNs converge upon glomeruli in the antennal lobe (AL,

analogous to the olfactory bulb) where excitatory projection

neurons (PNs, analogous to mitral cells) and local interneurons

(LNs), most of which are inhibitory, interact. PNs send excitatory

inputs to LNs, and LNs send rapid inhibitory feedback to PNs via

GABAA-like receptors. In locusts, honeybees, and Drosophila,

this feedback circuit has been shown to synchronize groups of

PNs, resulting in regular oscillating waves of output that depo-

larize Kenyon cells (KCs), the intrinsic neurons of the mushroom

body (MB). These waves can be detected as a local field poten-

tial (LFP; Laurent and Naraghi, 1994; Stopfer et al., 1997; Tanaka

et al., 2009).

We found that odors evoked oscillatory responses in the moth

Manduca sexta much like those described in the locust,

honeybee, and fly. Further, in the moth, we found that lengthy

odor pulses evoked oscillations that began at �40 Hz but then

suddenly decreased to �15–20 Hz. Simultaneous LFPs and

recordings from the moth’s antenna (electroantennogram,

EAG) showed that the net response intensity of ORNs decreased

in parallel to the shift in oscillation frequency. This suggested that

oscillation frequency might be determined by the intensity of the

response of the ORN population. In apparent contradiction,

though, we also found that odor-evoked oscillation frequency

remained remarkably constant across a broad range of odor

concentrations. What then is the relationship between stimulus

intensity and oscillation frequency?

Our approach, combining experimental and computational

methods, led to several conclusions. First, we found that the

frequency of odor-evoked oscillations in the moth olfactory

system is determined by the intensity of input to the oscillatory

AL network but that this intensity is determined by sensory adap-

tation and saturation of ORNs rather than by the intensity of

olfactory stimuli. Second, extending prior work, we demon-

strated that the vast majority of olfactory dynamic range is

encoded in the periphery by the number of responsive ORNs

rather than by the firing rates of those ORNs. And third, we char-

acterized a new stable oscillatory regime in which principle

neurons participating in an oscillatory network can fire much

faster than the oscillation frequency.

mailto:[email protected]

Neuron

Odor Intensity Coding and Oscillation Frequency

LFPEAG

A B

C

D E

F

Figure 1. Odors Evoked LFP Oscillations in the Moth MB and AL

(A) Recording site for LFP: center of the calyx in the MB. MB, mushroom body; mnsc, medial neurosecretory cells; OL, optic lobe; AL, antennal lobe.

(B) LFP oscillations (black traces) with simultaneously recorded electroantennogram (EAG, green traces) evoked by different pulse durations of 1% benzyl

alcohol, a plant volatile. Black horizontal bars: odor pulses. Color bars: time windows (500 ms) used to calculate the power spectra in (D).

(C) Brief odor pulses evoked fast oscillations; lengthy pulses evoked first fast, then slow oscillations. Normalized, average spectrograms from 18 trials obtained

from six animals with three trials each (see Experimental Procedures). Black horizontal bars above each spectrogram: odor pulses.

(D) Power spectra of oscillatory LFP responses averaged from 22 moths and eight odors, total of 820 trials. Color brackets: 14 Hz-wide bands used to calculate

the total oscillatory powers of fast (red, 30–44 Hz) and slow (blue, 10–24 Hz) oscillations in (E).

(E) Total oscillatory power of fast and slow LFP shifted significantly over lengthy odor pulses. Twenty trials tested for each odor were averaged before pooling,

mean ± SE, n = 41; two-way ANOVA: fwindow(2) = 26.62, p < 0.0001 (fast oscillations); fwindow(2) = 9.09, p < 0.0003 (slow oscillations). Asterisks: significant

differences (Tukey-Kramer multiple comparisons).

(F) LFP oscillations in the AL and MB were highly coherent. (Left) Example of odor-evoked LFP oscillations recorded simultaneously in the AL and MB; odorant:

1% cyclohexanone (4 s). Areas a and b are expanded in insets. Horizontal red (0.25–1 s) and blue (1–4 s) bars: times used for coherence analysis at right. (Right)

Magnitude squared coherence between the AL and MB. Thin black line: coherence of the response shown. Thick black and dotted lines: average coherence and

its one standard deviation range (five AL-MB combinations in four preparations, 20 trials each of two odorants), respectively.

RESULTS

Odors Evoke Fast and then Slow LFP Oscillationsin the MBTo characterize the moth olfactory system’s neural responses,

we delivered a variety of odors (nonpheromones, see Experi-

mental Procedures) over a wide range of concentrations and

a range of durations from 100 ms (as moths might experience

while flying in an odor plume) to 4 s (as moths might experience

when sampling food from flowers).

All odor stimuli in our panel induced robust oscillations in the

LFP recorded in the MB calyx (a target of PNs, Figure 1A).

Figure 1B shows an example of oscillations elicited by a presen-

tation of dilute benzyl alcohol vapor to the ipsilateral antenna of

a moth that was mostly intact but with its brain exposed for elec-

trophysiological recording (see Experimental Procedures). The

first of a series of odor presentations typically elicited only

weak oscillations in the LFP; however, oscillatory power in-

creased rapidly over the first four or five presentations (Figure S1).

Odor pulses briefer than�1 s elicited fast, 30–40 Hz oscillations in

the moth MB; notably, odor pulses longer than �1 s produced

oscillations that were initially fast but then dramatically slowed

to 10–20 Hz (Figures 1C–1E). Others (Laurent and Davidowitz,

1994; Perez-Orive et al., 2002; Perez-Orive, 2004) and we

(Figure S2) had previously observed similar but less pronounced

decreases in LFP oscillation frequency in the locust.

LFP Oscillations Are Generated in the ALWhere and by what mechanism are the oscillations generated?

In the moth, we made simultaneous recordings of LFPs from

Neuron 64, 692–706, December 10, 2009 ª2009 Elsevier Inc. 693

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the AL and the MB. All odors that we tested induced both fast

and slow oscillations in both the AL and the MB; further, the

AL-LFP and MB-LFP signals were highly coherent (n = 10,

Figure 1F).

We next made simultaneous intracellular recordings from pairs

of AL neurons together with LFP recordings from the MB

(Figure 2; all neurons morphologically identified by dye injection

and subsequent confocal imaging). Figure 2A shows an example

of a simultaneous recording of the MB-LFP, a PN, and an LN. For

most oscillation cycles, a spike in the PN was closely followed

(within�2 ms) in the LN by either a single spike or an EPSP, sug-

gesting that LNs received odor-driven periodic input from PNs.

And, reciprocally, the membrane potential of this PN revealed

a periodic hyperpolarization and depolarization after each spike,

suggesting that IPSPs from the inhibitory LNs regulated the

timing of spikes in the PN. Sliding-window cross-correlations

showed that the membrane potential fluctuations in this LN

and PN were tightly coupled to LFP oscillations recorded in the

MB (spikes clipped; Figure 2B). The oscillations slowed during

each trial.

Are the fast and slow oscillations generated in the AL? We

made intracellular recordings from 14 PNs and 30 LNs, each

simultaneously with LFPs recorded in the MB; Figure 2C displays

the spike-LFP phase relationships for spikes pooled from all

recorded cells. Spikes in PNs reliably phase locked to the LFP

at a point just past the peak of each cycle during fast (mean

direction and 95% confidence interval = 2.79� ± 9.1�; 1950

PN vs LFP

LN vs LFP

0.100.05

0.15

0.050.10

BA

C

D

Figure 2. PN and LN Responses Were

Strongly Phase Locked to the LFP

(A) Example simultaneous intracellular recordings

from PN and LN, with LFP recorded in the MB.

First 2 s after the odor onset shown; brackets:

portions expanded beneath. Odorant: 1% benzyl

alcohol.

(B) Subthreshold oscillations: five-trial average

sliding window cross-correlograms show reliable

LFP and subthreshold membrane potential oscilla-

tions for the PN (top) and LN (bottom) in (A). Spikes

were clipped. Vertical bars: odor pulses.

(C) Spike-LFP phase relationships: Polar histo-

grams show phase position, relative to LFP, of

spikes recorded in PNs (n = 14) and LNs (n = 30)

for fast and slow oscillations. Concentric circles:

firing probability. Black arrows: mean direction.

(D) All recorded neurons were filled with dye and

later morphologically identified. Example of PN

and LN morphology. An Alexa Fluor-633 (red) filled

PN and an Alexa Fluor-568 (yellow) filled LN are

shown. Scale bar: 50 mm. AN: antennal nerve.

spikes) and slow (23.4� ± 3.3�; 7005

spikes) oscillations. Spikes in LNs phase

locked to the LFP just after the PNs

during fast (71.4� ± 3.0�; 2623 spikes)

and slow (72.6� ± 1.1�; 12,723 spikes)

oscillations. The spike phase distribu-

tions of PNs and LNs were each signifi-

cantly different from uniform distributions

(Rayleigh test, p < 0.05), indicating strong

phase locking. The temporal relationships of these populations

match those shown in the simultaneously recorded example

(Figure 2A).

Together, the reliable, periodic relationships among AL

neurons suggested that the timed inhibition of PNs by LNs was

important for producing synchronous oscillations. To test this,

we selectively abolished fast inhibition from LNs to PNs by locally

injecting picrotoxin (PCT, a blocker of the GABAA-like inhibition

in Manduca, Waldrop et al., 1987) into the AL while recording

LFPs from the MB. Injection of PCT (n = 6) reversibly and sig-

nificantly reduced odor-evoked fast and slow oscillations;

control injections of saline (n = 5) had no effect (Figure S3).

Thus, inhibition from LNs within the AL is required for the gener-

ation of odor-elicited oscillations. Both fast and slow oscillations

are generated within the AL and are transmitted to the MB

by PNs.

Responses in KCs Are Shaped by OscillatoryInput from PNsTo test whether followers of PNs in the MB are sensitive to the

oscillatory synchrony of their input, we made intracellular record-

ings from a set of KCs (n = 20, all morphologically identified by

dye injection and subsequent confocal imaging).

During odor presentations, the membrane potentials of KCs

revealed pronounced subthreshold fluctuations that were tightly

coupled to simultaneously recorded LFP oscillations. In our four

recordings from KCs that revealed subthreshold activity, peaks


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of the membrane potential oscillations reliably occurred during

falling phases of the LFP oscillation (Figures 3A and 3B; see

Experimental Procedures). Further, odor-evoked spikes in KCs

were phase locked to the falling phases of LFP oscillations

A

B

C

D

Figure 3. Spiking in KCs Is Sparse, Odor Specific, and Tightly Phase

Locked to the LFP

(A) KCs showed odor-elicited subthreshold membrane potential fluctuations

that were tightly correlated with LFP oscillations. Example: top, gray: LFP;

bottom, black: simultaneous intracellular record of a KC. Bottom: details of

fast and slow periods during oscillatory response. Odor: 4 s, 1% benzyl

alcohol. Gray broken line: resting potential.

(B) Cross-correlations between LFP oscillations and KC subthreshold activity.

Cross-correlation was calculated for times bracketed in (A). Black lines: corre-

lation for the trial shown in (A); gray lines: 21 other trials from this cell. All eight

KCs showing subthreshold oscillations revealed similarly shaped correlation

functions, three with coefficients >0.3.

(C) Polar histograms show strong phase locking between spikes in KCs and

the LFP oscillations. Histograms show spikes recorded from 20 KCs during

fast and slow oscillations. Arrows: mean phase position.

(D) Example of KC morphology; posterior view of MB; KC filled with Alexa

Fluor-633. Scale bar: 50 mm. Arrow: soma; CaM: medial calyx; CaL: lateral

calyx.

during fast (117.1� ± 12.2�; 329 spikes) and slow (125.7� ±

5.8�; 706 spikes) oscillations (Figure 3C). The spike phase distri-

butions for KCs, like those of PNs and LNs, were significantly

different from uniform distributions (Rayleigh test, p < 0.05).

We found that the timing of spikes in PNs, LNs, and KCs

became more precise (less jitter around the preferred phase)

as the oscillation frequency decreased (Figure S4). Together,

these results indicated that oscillations strongly influence the

timing of spikes in the KCs.

Oscillation Frequency Remains Constant over a WideRange of Odor ConcentrationsWe had observed that long odor pulses elicited oscillations that

shifted dramatically in frequency. What causes this shift? We

found that, during long odor pulses, EAGs decreased in ampli-

tude with timing roughly matching that of the frequency shift in

the LFP (Figure 1B). The decrease in EAG amplitude was prob-

ably caused by sensory adaptation within the ORNs (Kaissling

et al., 1987), a mechanism that reduces the intensity of response

to an ongoing stimulus. The nearly parallel changes in ORN

output intensity and oscillation frequency suggested to us that

the intensity of the stimulus may determine oscillation

frequency.

To test this, we delivered a wide range of concentrations of

three odors (hexanol, octanol, and geraniol), expecting to find

that higher concentrations elicited more intense responses

from ORNs and perhaps faster oscillations in the LFP. Indeed,

the range of odor concentrations we used elicited a wide

range of responses in the EAG (Figures 4A and 4B) and in the

LFP (Figure S5) from small, near-basal fluctuations to deep,

saturating deflections; thus, the range of odor concentrations

that we used effectively elicited a wide range of response

intensities from the population of ORNs. Lower odor concen-

trations evoked weaker LFP oscillations; higher concentrations

evoked stronger oscillations (Figure 4C). However, we found

that the initial LFP oscillation frequency remained almost con-

stant across five or more orders of magnitude of odor concen-

tration (Figure 4D). Together, these results appeared contra-

dictory: decreasing drive from ORNs appeared to result in

dramatically reduced oscillation frequency, yet experimentally

changing the intensity of the input to ORNs had little or no

such effect.

The ORN Population Encodes Odor ConcentrationSpatially and TemporallyThe EAG aggregates the responses of many ORNs in the

antenna. Thus, we next characterized the responses of individual

ORNs on the moth antenna while delivering odor pulses of

different concentrations (Figure 5; n = 37 ORNs from 9 prepara-

tions; see Experimental Procedures). We found that individual

responsive ORNs revealed a small dynamic range, firing at rates

that varied only within narrow spans of concentration. ORNs

responding to moderate odor concentrations (e.g., 0.01%–1%

of hexanol; see Experimental Procedures) showed firing rates

that quickly saturated (Figure 5F, green lines) or even decreased

(Figure 5F, red lines) as odor concentration increased. And ORNs

that initially responded vigorously to an odor presentation (e.g.,

with firing rates >40 Hz) quickly slowed their firing (Figures 5B


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and 5C). This sensory adaptation was evoked by all odors tested

and all concentrations whenever the initial firing rate exceeded

�40 Hz (Figures 5D and 5E). Faster-firing ORNs underwent

greater adaptation (Figure 5E), suggesting that ORNs better

tuned for a given odor would adapt more. Thus, we found that

each ORN fired at a rate tightly constrained by adaptation and

saturation.

To quantify the dynamic range of individual ORNs relative to

that of the population, we fit concentration response curves

with the Hill equation (Figures 5F and 5G; Firestein et al.,

1993; Wachowiak and Cohen, 2001; Koulakov et al., 2007).

In our sample of ORNs and odors, we found that response

thresholds were widely distributed across concentrations

spanning about six orders of magnitude (C10, Figure 5H).

Consistent with this, increasing numbers of ORNs participated

in the response as odor concentrations increased (Figures 5F

and 5H). And most ORNs had Hill coefficients greater than 1

(mean = 1.1269; median = 0.802), corresponding to a dynamic

range spanning less than two orders of magnitude (Figures 5I

and 5J; Koulakov et al., 2007). The two orders of magnitude

encoded by individual ORNs corresponded to only about 2/6,

or 33%, of the dynamic range provided by the whole ORN

100%

1%

0.01%

0.0001%

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Octanol (%)0.0018

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Geraniol (%)

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Hexanol (%)

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0.4 mVHexanol(%)

Figure 4. Odor Concentration Determines

Oscillation Coherence, Not Frequency

(A) EAG traces revealed total ORN output

increased with odor concentration. Example from

one antenna; horizontal bar: 4 s.

(B) Summary. EAG amplitude (first 1 s, see bracket

in A) evoked by a range of odor concentrations.

Mean± SE; n= 8; two-way ANOVA: fodor_concentration =

16.84, p < 0.0001.

(C) Higher concentrations of odor evoked stronger

LFP oscillations. Initial portions of the odor

response are shown. Scale bar: 50 ms.

(D) The frequency of fast oscillation changed not

at all or only slightly across a broad range of

odor concentrations. All results are shown (dots);

bar graph shows means, n = 9. Leftmost bars:

basal oscillatory power in absence of odorant.

Hexanol: two-way ANOVA: fhexanol_concentration =

6.16, p < 0.001; post hoc Tukey-Kramer tests

found small but significant differences between

three highest and two lowest concentrations

(p < 0.05). Octanol: foctanol_concentration = 4.98,

p < 0.001; post hoc tests: significant differences

between highest two and lowest two concentra-

tions of octanol (p < 0.05); Geraniol: two-way

ANOVA: fgeraniol_concentration = 1.4, p > 0.25, ns.

population. Further, we found that the

firing rates in the ORN population fit

Gaussian distributions (Figure 5K). As

odor concentration increased, the width

of the distribution (number of responsive

ORNs) broadened but the height of the

distribution (firing rate) remained about

the same (Figure 5K). These results

indicate that, in the moth, the great

majority of olfactory dynamic range is

encoded as changes in the size of the population of respon-

sive ORNs.

Firing Rate Adaptation in ORNs DeterminesOscillation FrequencyOur analysis of individual ORNs revealed that the frequency transi-

tion in LFP oscillations followed a temporal profile closely matching

that of the adaptation rate of the most active ORNs (Figures 5L and

S6). Yet, experimentally changing the intensity of input to the ORNs

(odor concentration) had little if any such effect. To explain these

apparentlycontradictory findings and tounderstandhowoscillation

frequency is determined, we incorporated our physiological mea-

surements into a full-scale, map-based network model (reduced

type, Rulkov, 2002; Rulkov et al., 2004; Rulkov and Bazhenov,

2008) of the moth AL (Figure 6A). We simulated input to the AL

network as synaptic currents applied to odor- and concentration-

specific populations of PNs and LNs (Assisi et al., 2007; see Exper-

imental Procedures). In our model, as in vivo, this input caused the

population of PNs to spike and to synchronize through feedback

inhibition mediated by LNs (Figure 6B). Synchronized spiking in

the model AL was manifest as periodic oscillations of the LFP

(Figure 6B, top; calculated as the average activity of all PNs).


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We had found that the adaptation of ORN firing rates followed

a temporal profile matching that of the frequency transition in

LFP oscillations (Figures 5L and S6). How does adaptation

influence the dynamical properties of the AL network? To simu-

late activation and adaptation of the odor responses of ORNs,

we drove our network model with a rapidly rising and then slowly

decaying input (Figure 6B, bottom) with the size of the AL popu-

lation receiving external stimulation (input ‘‘width’’) held

constant. During the simulated odor’s onset, the rapid increase

in input intensity quickly entrained the network to generate

�40 Hz oscillations (Figures 6B and 6C). The subsequent

decrease in stimulus amplitude initially led to a reduction in the

LFP amplitude, signaling a decrease in the synchrony of spiking

across the population of responsive PNs. But as the input inten-

sity continued to decrease, synchrony suddenly resumed,

although now at �20 Hz. During this transition, the interspike

interval (ISI) distributions of both PNs and LNs (Figures 6C and

6D) lengthened. Our intracellular recordings from PNs and LNs

had revealed qualitatively similar changes in ISI distribution

(Figure S7). In our model, a 40%–50% decrease in stimulus

intensity caused a frequency shift (Figure 6B) matching what

we had observed in vivo (Figures 1D and 1F). This result sug-

gested that a change in stimulus intensity similar to what occurs

in vivo, and not the size of the responsive ORN population, could

explain much of the change in oscillation frequency. Other

factors such as the strengths and the time constants of synaptic

currents could influence oscillation frequency as well (Figure S8).

To test the range of possible responses in the AL, we next

analyzed the steady-state network dynamics of our model as

a function of input intensity. Throughout these stimulations we

held constant both the size of the AL population receiving

external input and the amplitude of the input; in separate exper-

iments we systematically changed the input amplitude to LNs

and PNs to explore a broad space of parameters. Our model

showed that the AL network could generate oscillations with

a wide range of frequencies, including 20–40 Hz, depending on

the net intensity of its input (Figure 6E, left panel). Further, indi-

vidual PNs and LNs could change average firing rate as a function

of excitatory and inhibitory input intensity (Figure 6E, middle and

right panels). In our model, inhibitory LNs almost always spiked

at the frequency of the LFP oscillations; notably, excitatory

PNs could fire faster with either one or two spikes during each

oscillatory cycle (Figures 6C and 6D). These results match those

of our intracellular recordings (Figure S7).

How do changes in odor concentration influence the dynam-

ical properties of the AL network? Our model had shown that,

for a network with a fixed number of responsive neurons,

increasing the amplitude of external stimuli led to a progressive

increase in oscillation frequency (Figure 6E). But our recordings

from ORNs had shown that, as the concentration of an odorant

increased, more types of receptors began to respond (Figure 5K;

see also Stewart et al., 1979; Duchamp-Viret et al., 2000;

Wachowiak and Cohen, 2001; Hallem and Carlson, 2006). To

simulate this effect of changing odor concentration, we varied

the proportion of the PN and LN populations (parameter s, width

of the curve in Figure 7A; compare to Figure 5K) driven by

external excitatory input. We found that varying the size of the

stimulated neuronal population only slightly varied the frequency

of oscillations (Figures 7B–7D). When driven by very low odor

concentrations (‘‘narrow’’ input, i.e., s = 0.2), the frequency of

LFP oscillations increased slowly upon odor onset (Figure 7C,

left); several oscillatory cycles were required to engage all the

neurons in oscillatory dynamics. Our model suggested that

the main effect of varying the size of the responsive neuronal

population was to vary the coherence of the moth AL network,

but not its frequency.

Because sensory input to our model was simulated using

a Gaussian profile, when input underwent adaptation, two

factors changed: (1) active PNs decreased their firing rates,

and (2) the size of the active PN population decreased (Figure

6C). To test which factor most directly underlies the LFP’s

frequency shift, we provided our model a simplified square input

profile rather than a realistic Gaussian input profile; the simplified

input drove all stimulated PNs and LNs identically and gave zero

input to all nonstimulated PNs and LNs, thus holding the size of

the active PN population constant over time even as the input

adapted. With this constrained input, adaptation still caused

the oscillatory frequency to decrease (Figure S9A). In contrast,

decreasing the size of the stimulated AL population (to model

a decrease in odor concentration) did not affect oscillation

frequency (Figure S9B). Consistent with this result, an even

simpler model consisting of only a single PN and a single LN,

reciprocally coupled (Figure 7D), showed that changing the

intensity of the input caused a shift in oscillation frequency (Fig-

ure 7E). Taken together, these models suggest that input inten-

sity regulates the firing frequency of active PNs, which directly

determines the network oscillatory frequency.

A Subset of Strongly Activated PNs RegulatesOscillatory FrequencyTo test the robustness of our results and to gain a more intuitive

understanding of the mechanism that underlies the oscillatory

response transition in the AL, we designed an additional, simpli-

fied ‘‘firing rate’’ version of our more realistic map-based model

of the AL network (see Experimental Procedures).

To test whether the oscillatory frequency of the AL network is

determined by the firing rates of activated PNs, we systematically

varied the threshold required to activate PNs, effectively removing

weakly activated ORNs fromthe network (Figure 8A). Even though

this manipulation (like decreasing odor concentration) greatly

decreased the size of the active population of neurons and

caused the overall input to the network to change dramatically

(Figure 8B), the oscillatory frequency remained constant (Fig-

ure 8C). Next, we simulated the effect of sensory adaptation by

altering the response intensity of the most strongly activated

PNs (Figure 8D). This manipulation, which kept the number of

active neurons constant but reduced overall input to the network

(compareFigures8B and 8E), greatly altered oscillatory frequency

(Figure 8F), consistent with results we obtained with our spiking

map-based model and with our physiology experiments.

Further, our simplified rate model showed that adaptation of

the ORNs was sufficient to shift the oscillatory frequency of the

AL network (Figures 8G and 8H); a version of the model lacking

adaptation showed no shift in frequency (Figures 8I and 8J).

These results, combined with those of our physiological record-

ings and spiking model show that, for any given odor or


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A

0.001

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0.1

1

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ORN3 ORN7 ORN11B

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0.0001%0.001%0.01%0.1%1%10%100%

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Time (s)

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Firin

g ra

te (H

z)

20ORN #

100.0%0.1%

concentrationodor

4 s

*

F1

F2

Pop

ulat

ion

firin

g ra

te (H

z)

0 2 4Time (s)

150

0

50

100

L

20

40

0 2 4Time (s)

Osc

illat

ion

frequ

ency

(Hz)

50

100

150 OR

N m

aximum

firing rate (Hz)

ED

10-4 10 -3 10 -2 10 -1 100 101 1020

20

40

Odor concentration (%)

Firin

g ra

te (H

z) C10 C90

Dynamic range log (C90/C10) = 1.1 orders of magnitude

Fmax

Hill coefficient = 1.7251

Odor concentration (%)

0

50

ORN3

ORN7

n=37

Incr

ease

in

firin

g ra

te (H

z)

ORN11

25

10-4 10 -3 10 -2 10 -1 100 101 102

6

Figure 5. Saturation and Adaptation Constrained the ORN Firing Rates

(A) Example extracellular recordings from a sensillum on the antenna show responses to odor pulses (4 s) of 10% hexanol (top) and jasmine oil extract (bottom).

Two ORNs were recorded in this sensillum, one with short spikes and sustained firing, and one with large, transiently firing spikes (marked by *). Tan bars: odor

pulses.

(B) Spike rasters of three ORNs tested with a wide range of concentrations of hexanol. Blocks of ten trials for each concentration were tested in random order.

Tan bars: odor pulses (4 s).

(C) Instantaneous firing rates of a representative ORN. Spikes were binned (100 ms); spike count in each bin averaged over ten trials.

(D) The most active ORNs quickly adapted. Instantaneous population firing rate; firing rate averaged over ten trials for each odor-sensillum combination;

1011 odor-sensillum combinations (32 sensilla tested with up to 20 odors each). Responses to odor-sensillum combinations were divided into two groups

based on initial peak firing frequency (>40 Hz: light gray; < 40 Hz: dark gray). Brackets: 1 s analysis bins used to calculate initial (F1) and late peak (F2) frequencies.

For this analysis multiunit activity was included.

(E) Relationship between peak frequencies F1 and F2. Dots under the diagonal line indicate adaptation. Almost all odor-sensillum combinations showing initial

spike frequency >40 Hz (F1) underwent adaptation during the stimulus.

(F) Concentration tuning curves for 22 ORNs. Mean firing rates of most ORNs saturated after the odor onset. Red traces: ORNs with firing rates that decreased

after the peak concentration; Green traces: ORNs with firing rates that saturated after the peak concentration.

(G) ORN concentration response curves were fit with the Hill equation. Example: ORN22, tested with different concentrations of hexanol. Parameters (C10, C90,

Hill coefficient, Fmax) in panels (H)–(J) were obtained from this fitting.

(H) Lack of correlation between maximum firing rates (Fmax) and the thresholds (C10) of individual ORNs. Response thresholds (C10) spanned about six orders

of magnitude, indicating our sample of ORNs, as a population, offered a wide dynamic range. Only responsive odor-ORN combinations (n = 25, > 5 Hz change

in mean firing rate during odors) were included in this analysis.


Neuron


0.5 s

LFP

PNLN

Input 1 2

0 20 40 60 80 100

Time (ms) Time (ms)

PN-ISIfast

LN-ISIfast

PN-ISIslow

LN-ISIslow

200400600800

500 1000 1500 2000 2500

100200300

500 1000 1500 2000 2500

Time (ms)

PN

LN

B

C

Input

A

D

0 20 40 60 80 100

0 20 40 60 80 100 0 20 40 60 80 100

0.9

0.7

0.5

0.3

0.1 102030405060

102030405060708090

0

10

20

30

40

50

LFP

Input to LN

2 22

1 11PN LN

0.1 0.3 0.5

Hz Hz Hz0.9

0.7

0.5

0.3

0.1

0.9

0.7

0.5

0.3

0.1

0.1 0.3 0.50.1 0.3 0.5NL ot tupnINL ot tupnI

Inpu

t to

PN

E

Figure 6. Odor-Evoked Oscillations in Model of Moth AL

(A) Full-scale, map-based model included randomly connected populations of 820 PNs and 360 LNs. Odor pulse input was simulated by external currents

delivered to a subset of neurons.

(B) Amplitude of the input was set to resemble the EAG (bottom). LFP (top) and neuronal (middle) responses resembled those recorded in vivo. The input to the

model was tuned to match results of our physiological recordings and corresponded to points ‘‘1’’ and ‘‘2’’ in the parameter space shown in (E).

(C) Raster plots show spikes in all PNs (top) and all LNs (bottom) evoked by one odor pulse (applied from 500 to 2500 ms).

(D) Interspike interval (ISI) distributions during fast and slow phases of LFP oscillations. Many PNs fired two spikes in a single oscillatory cycle (ISI < 25 ms during

fast and ISI < 50 ms during slow phase); LN frequency was typically limited to the LFP frequency.

(E) Frequency of LFP, PN, and LN oscillations as a function of input from ORNs to PNs and LNs. Sweeping the points between ‘‘1’’ and ‘‘2’’ in parameter space

mimicked the changes in the ISI distribution (compare D and Figure S7) and the abrupt change in oscillatory frequency (compare B and the Figure 1C) we

observed in vivo.

concentration, oscillation frequency is controlled by a small

subset of ORNs and PNs, those that are most highly responsive.

In summary, our computational models (Figures 6–8) demon-

strated that the shifts in LFP frequency that we observed in vivo

during lengthy odor stimulations can be explained by gradual

changes in the intensity of output from a stable group of ORNs

to the AL. This intensity level is determined mainly by the adapta-

tion and saturation of the peripheral receptor neurons (ORNs)

(I) Hill coefficient (red) and dynamic range (blue) as function of threshold. ORNs responding to low concentrations typically showed low Hill coefficients and

relatively wide dynamic ranges.

(J) Histogram of Hill coefficients. Most ORN-odor combinations showed Hill coefficients >1, indicating a dynamic range <2 orders of magnitude.

(K) Firing rates in the ORN population followed Gaussian distributions. The numbers of spikes in the first 1 s of odor responses (indicated by colored dots)

were counted in 37 ORNs tested with hexanol. The ORN firing rates were fit with Gaussian distributions (colored lines). As the odor concentration increased,

the width of the distribution (sigma) broadened but the height of the distribution remained about the same. All odor concentrations evoked responses with

Gaussian distributions.

(L) Frequency of MB-LFP oscillations changed in parallel to the odor input (1% hexanol) to the AL network. Odor input: firing rate of the most active ORN (at each

50 ms time slice across 22 ORNs). Power spectrogram: average of nine preparations.


Neuron


C

Time (s) Time (s)

2030405060

0.5 1.0 1.5 2.0 2.5

= 0.2 = 0.4

zH 04zH 04

0.5 1.0 1.5 2.0 2.5

0.5 s

0.5 1.0 1.5 2.0 2.5Time (s)

40 Hz

= 0.6

= 0.2 = 0.4 = 0.6

A

B

D

D E

Figure 7. Effect of Odor Concentration upon LFP Frequency in Moth AL Model

(A) Odor input to the network was simulated by synaptic currents applied to an odor-specific population of PNs and LNs. The size of stimulated population

(defined by a Gaussian distribution with width s; see Figure 5K) was varied to simulate different odor concentrations.

(B) Examples of LFP oscillations elicited by three odor concentrations. As in vivo, during lengthy odor stimuli the network shifted from fast to slow oscillatory

states. LFP was band-pass filtered (5–50 Hz).

(C) Spectrograms of LFP oscillations (those shown in B) for three odor concentrations.

(D) Minimal network consisting of a single PN and LN.

(E) Frequency of oscillations in the minimal network increased sublinearly as a function of input amplitude.

rather than by the intensity of the environmental stimulus (odor

concentration). Our results show that, in the periphery, the great

majority of the olfactory system’s dynamic range is encoded by


the size of the responsive receptor population rather than by its

firing rate. Our results also resolve an apparent contradiction,

that oscillation frequency follows the intensity of the net receptor

Neuron


output (amplitude of the EAG) but not the concentration of the

odor. These findings are summarized in Figure 9.

DISCUSSION

Odor-Elicited Oscillations in the MothIn the moth Manduca sexta, our intracellular recordings from PNs,

LNs, and KCs together with recordings of the LFP from the MB

and AL (Figures 1–3) revealed that moths employ essentially the

same neural mechanism as that characterized in the locust and

Drosophila: oscillations are generated in the AL via GABAA-type

inhibition (Figure S3), build up gradually over repeated odor

presentations (Figure S1; Stopfer and Laurent, 1999), and influ-

ence the fine spike timing of downstream KCs (Laurent, 2002;

Perez-Orive et al., 2002; Assisi et al., 2007; Tanaka et al., 2009).

This result contradicts several earlier reports. Previously, in

the moth, pulses of pheromone were found to induce highly local-

ized LFP oscillations only within the AL, with spikes in pheromone-

sensitive PNsphase locked to theAL-LFP oscillations (Heinbockel

et al., 1998). However, such stimuli were described as never pro-

ducing coherent LFP oscillations between the MB and the AL

(Christensen et al., 2003). Further, in a multiunit recording experi-

ment (Christensen et al., 2000) and a double intracellular recording

experiment (Lei et al., 2002), cross-correlation analyses detected

1.2 1.0 0.8 0.6

10

30

50

0.2 0.4 0.6 0.8

30

40

50Fast Oscillation

Slow Oscillation

Threshold10 30 50 70

0.20.40.60.81.0

PN #

OR

N F

iring

Rat

e

0.00.40.8

1.2

0.81.0

Scale

scale = 1.2

thresh = 0.0

0.8

Summed inputto AL

0.6

CBA

FED

thres hold

s cale

1 2 3 4 5Time (s)

1 2 3 4 Freq

uenc

y (H

z)

Am

plitu

de

Summed inputto AL

10 30 50 70PN #

0.20.40.60.81.0

OR

N F

iring

Rat

e

Am

plitu

de

1 2 3 4 5Time (s)

1 2 3 4 Freq

uenc

y (H

z)

FastOscillation

SlowOscillation

10 20 30 40 50Frequency (Hz)

LFP

Pow

er

LateEarly

EAG Odor Pulse(3 sec)

LFP

EAG

LFP

EarlyLate

HG

JI

Early Late

Early Late

Odor Pulse(3 sec)

LFP

Pow

er

10 20 30 40 50Frequency (Hz)

Figure 8. Simplified Firing-Rate Model of

the Moth AL

(A–C) Varying the width of the distribution of

responsive PNs (simulating changes in odor

concentration, see Figures 5K and 7A) had no

effect on oscillation frequency. (A) Width was

varied by adjusting the threshold level for acti-

vating PNs. (B) Adjusting the threshold greatly

altered overall input to the modeled AL network.

(C) The oscillation frequency remained constant

despite simulated changes in odor concentration.

(D–F) Varying the height of the distribution of

responsive PNs (simulating adaptation in ORNs)

caused changes in oscillation frequency. (D)

Height was altered by scaling the response inten-

sity of activated PNs. (E) Adjusting the intensity

greatly altered overall input to the modeled AL

network, as in (B). (F) The frequency of LFP oscilla-

tions decreased when adaptation of ORNs was

simulated.

(G and H) Model EAG (green) and LFP response

(black) when ORNs are permitted to adapt. Adap-

tation alone is sufficient to shift the oscillatory

frequency (power spectra for early and late oscilla-

tions shown in H).

(I and J) Model EAG (green) and LFP response

(black) when ORNs are not permitted to adapt.

Without adaptation oscillation frequency remains

constant (power spectra in J).

no sustained oscillatory synchrony

between pairs of PNs but rather only

brief, stimulus-locked, nonoscillatory

synchrony. These observations led to

the proposal that, in Manduca, only tran-

sient, nonoscillatory synchronous activity

among PNs supports odor coding, likely by promoting coinci-

dence detection by downstream elements (Lei et al., 2002). Our

experiments employed general, nonpheromonal odors, such as

host plant volatiles and common food blends at a wide range of

concentrations. The differences in our results from those reported

earlier probably arise both from our focus on the general olfactory

system rather than the pheromone system and from differences in

recording techniques (likely the electrode’s shape and internal

solution; see Experimental Procedures). The moth pheromone

system, which, within the AL, consists of three specialized

glomeruli anatomically separate from the �60 glomeruli of the

general odor system (Rospars and Hildebrand, 1992), may not

provide an ideal model for all aspects of general olfaction.

Indeed, our results show that, to a remarkable extent, odor-

coding mechanisms in Manduca are similar to those of other

species, including Drosophila (Tanaka et al., 2009), honeybee

(Stopfer et al., 1997), and locust (Laurent and Naraghi, 1994;

MacLeod and Laurent, 1996; Perez-Orive et al., 2002). This

was perhaps unexpected because these species differ in details

of olfactory anatomy and physiology. The�60 ordinary glomeruli

in the AL of Manduca compare roughly in number to many other

insects (Anton and Homberg, 1999), and the great majority of its

PNs are uniglomerular (Homberg et al., 1989). By contrast, in the

locust, the AL is organized into �1000 microglomeruli (Ernst


Neuron


0

1

OR

N fi

ring

rate

ORN

repertoire

Long odor stimulus(causes sensory adaptation)

Response over timeResponse to each stimulus

Reduce odor concentration(activates fewer ORNs)

Drive to the most active PNs Drive to the most active PNs

PFLPFL

A1

A2

A3

A4

B1

B2

B3

B4

Figure 9. Summary of the Mechanism to

Determine Oscillation Frequency

(A1) Long odor pulses cause ORNs to undergo

sensory adaptation.

(A2) When odor exposure is lengthy, active ORNs

adapt, decreasing their firing rates.

(A3) The lower ORN firing rates reduce excitatory

drive to PNs.

(A4) As each PN receives less intense input, its

firing rate decreases and oscillations slow.

(B1) When odor concentration is reduced, smaller

populations of ORNs respond.

(B2) However, the responsive ORNs continue to

fire at high rates.

(B3) Thus, the most active PNs continue to receive

strong input from responsive ORNs.

(B4) And oscillation frequency remains stable

across broad ranges of odor concentration.

et al., 1977), which are heavily interconnected through multiglo-

merular PNs (each visiting 12–24 glomeruli) and extensively

arborized LNs (MacLeod and Laurent, 1996). In Manduca LNs

generate full-size sodium spikes. But in the locust, LNs produce

graded calcium potentials rather than all-or-none spikes.

Because of its microglomerular structure and extensive multiglo-

merular connectivity, the locust olfactory system has sometimes

been described as atypical (Hansson and Anton, 2000). Never-

theless, our results strongly suggest that, despite substantial

differences in anatomical detail, the olfactory systems of these

species function in a remarkably similar fashion.

Despite the striking similarities in odor-coding mechanisms in

locust and moth, we found small differences. The oscillatory

phase relationship between spikes in PNs and LNs is slightly

different in the two animals, possibly because of differences in

the timing of spikes in LNs. In the locust the population of PNs,

spikes with the greatest synchrony upon odor onset (Mazor and

Laurent, 2005) probably because the strong, nonadapted input

can activate many LNs, which coordinate the spike timings of

PNs (Assisi et al., 2007). In the moth, we found that odor inputs

were strongest at the odor onset as well (Figures 5C and 5D).

However, both across LNs and PNs, synchrony increased grad-

ually over the course of a response (Figure S4). This is probably

because, in the moth, oscillation frequency at the odor’s onset

shifted too quickly to permit full entrainment of the oscillatory

network. Indeed, frequency shifts that we observed in the moth

over the course of a stimulus were typically greater than those

in the locust (Figure S2; see also Perez-Orive, 2004). Our simpli-

fied rate model suggests this difference could be explained by

greater net inhibition in the locust: we found that if we slightly

increased the strength of inhibition in our simplified model of

the moth AL, the model then produced frequency shifts similar

to those observed in the locust (Figure S10). We speculate that,

compared to the moth, the balance of net excitation and inhibition

is slightly shifted toward stronger inhibition in locust.


Adaptation and Saturation of ORN Firing Rate Determinethe Oscillation FrequencyOur recordings revealed that additional ORNs were recruited into

the responsive population as odor concentration increased

(Figure 5), a result consistent with a fundamental property of

receptors: they become less selective as the concentrations of

ligands increase. Yet we found the range of response intensity

of these ORNs was sharply constrained. Long odor pulses

caused the most highly responsive ORNs to rapidly adapt their

firing rates, with a time course similar to that of the shift in oscil-

lation frequency (Figure 5L). Further, the firing rates of the most

precisely tuned ORNs saturated when stimulated by low to

moderate odor concentrations (Figures 5C–5F).

Our electrophysiological and computational approaches

allowed us to compare the relative contributions of the size of

the responsive population and its response intensity. We found

that in the periphery, coding of odor concentration was heavily

dominated by the size of the set of responsive ORNs rather than

by the intensity of the response of the ORNs. At low odor concen-

trations, only those receptors most precisely tuned to the odor re-

sponded; as the concentration increased, the precisely tuned

ORNs continued to fire but quickly adapted and saturated and

thus displayed strictly constrained increases in response inten-

sity. However, additional, less well-tuned ORNs began to partici-

pate in the response, thus encoding the concentration of the odor.

Several lines of evidence indicate that information about odors

is encoded by a population of ORNs in a combinatorial fashion

(Buck, 1996). A recent comprehensive study of all the receptor

types on the Drosophila antenna (Hallem and Carlson, 2006)

showed that the firing rates of ORNs often saturated at moderate

concentration, that some ORNs decreased their firing rates at

extremely high concentrations, and that, at high concentrations,

individual ORNs tended to respond broadly to many odors.

Studiesusing 2-deoxyglucose labeling, c-fos, and calcium images

have shown that the spatial pattern of glomerular activation can

Neuron


expand as odor concentration increases (for review see Buck,

1996). Further, several studies suggest that ORNs can respond

within a narrow dynamic range (Firestein et al., 1993; Stewart

et al., 1979; Koulakov et al., 2007). Indeed, a theoretical study of

the locust olfactory system predicted that an intensity coding

scheme like that shown here could explain the invariant frequency

of odor-evoked oscillations over a wide range of stimulus intensity

(Assisi et al., 2007). These results are consistent with our quantita-

tive finding that odor intensity is encoded mainly by the size of

active ORN population rather than by firing rates.

We incorporated our findings in the moth into two types of

computational models to determine how sensory input to an

oscillatory circuit influences its frequency. Our models robustly

mimicked the frequency transition that we observed between

fast and slow oscillatory states as input intensity gradually

decreased (Figures 6–8 and S10). Further, our models demon-

strated that recruiting additional, but less well-tuned, ORNs

could simulate responses to higher odor concentrations while

causing only minimal changes in oscillation frequency (Figures

7 and 8), similar to what we observed in vivo (Figures 4 and 5).

Our models also demonstrated how oscillation frequency can

shift between fast and slow states (Figures 6 and 8), depending

mainly upon the varying output intensity of rapidly saturating and

adapting receptors, rather than upon odor concentration.

In agreement with earlier work in locust (Stopfer et al., 2003),

our results show that increases in odor concentration led to large

increases in the coherence of the odor-triggered oscillatory

synchrony of PNs (Figure 4C). This large increase in coherence

was accompanied by only small changes in the frequency of

oscillation (Figure 4D) and was caused mainly by increasing

the size of the activated ORN population. Our results show

that, in the moth AL, the coherence and the firing rate of the

PN ensemble are determined independently (for a discussion

of theory see Salinas and Sejnowski, 2001). This independence

enables an efficient strategy for dynamically matching the firing

properties of PNs to the coincidence detection-based decoding

properties of KCs (Perez-Orive et al., 2002, 2004).

What are the implications of this transition during an odor

response? A comparison of the jitter in spike timing relative to

the LFP before and after the frequency transition revealed an

increase in spike time precision in LNs, PNs, and KCs (Figure S4).

Because little is known about how the output of KCs is decoded

by cells that follow them, potential benefits of this increase in

spike precision are not immediately apparent. One possibility

is that the increase in the synchrony of input to the KCs might

help sustain highly specific firing in these cells even though the

output of PNs decreases when ORNs adapt.

A similar frequency transition from gamma to beta oscillations

has been noted in the rat olfactory bulb (Neville and Haberly,

2003), but the mechanism underlying the transition is quite

different from that shown here. In the rat, oscillations of different

frequency are generated by different neural circuits: odor-

evoked gamma oscillations in the olfactory bulb arise locally,

but beta oscillations require the participation of the olfactory

cortex (Neville and Haberly, 2003).

It is well established that shifts in the balance of excitation and

inhibition (Brunel and Wang, 2003) or changes in excitatory drive

(Whittington et al., 1995; Traub et al., 1996) can influence the

oscillation frequency of a neural network. However, sensory

systems characterized in vivo often generate oscillations of

invariant frequency when driven by a wide range of stimulus

intensities (Bringuier et al., 1997; Stopfer et al., 2003; Schadow

et al., 2007). Our results suggest that the extent to which oscilla-

tion frequency is sensitive to stimulus intensity depends at least

in part on the properties (such as adaptation and saturation) of

the neurons that provide inputs to the oscillatory network. In

the retina, for example, some classes of ganglion cells have

been shown to increase their firing rates as the velocity of a

moving visual stimulus increases (Cleland and Harding, 1983);

concomitantly, the frequency of gamma oscillations in the visual

cortex monotonically increases (Gray and Prisco, 1997). On the

other hand, in cortical areas responsive to the orientation or

direction of a visual stimulus, oscillation frequency remains

constant (Gray and Singer, 1989), likely because changing these

stimuli only changes the population of active cells. That many

primary sensory neurons display tuning, saturation, and adapta-

tion characteristics may help explain why invariant oscillation

frequency is often observed in sensory systems (Bringuier

et al., 1997; Stopfer et al., 2003; Schadow et al., 2007).

Oscillatory Dynamics and Fast-Firing Principal NeuronsFast 20–60 Hz synchronized oscillations are common in neuronal

circuits. In one form of gamma oscillations (interneuron network

gamma, ING), a network of mutually inhibiting interneurons

exclusively establishes the rhythm; pyramidal cells are simply

entrained to it, and their low firing rates have little or no effect on

network oscillations (Whittington et al., 2000; Wang and Buzsaki,

1996). But in our models oscillations failed when synaptic input

from PNs to LNs was blocked (data not shown). This suggests

that odor triggered oscillations in the moth AL are not entirely

mediated by an ING-type inhibitory network but rather require

the active participation of excitatory PNs to drive LNs (indeed, we

observed that moth PNs fired slightly before LNs; Figure 2C),

which in turn synchronized PNs through feedback inhibition.

In this respect, odor-triggered oscillations in the moth AL are

similar to the persistent/transient forms of gamma oscillations

(pyramidal-interneuron network gamma, PING; Borgers et al.,

2005; Borgers and Kopell, 2003, 2005) in the vertebrate cortex

and hippocampus.

Our intracellular recordings from the AL network revealed,

however, an unusual situation: most active PNs fired faster

than the oscillation frequency (Figure S7). More typically, as in

the case of transient gamma oscillations induced by tetanic stim-

ulation of the hippocampus (Traub et al., 1996; Whittington et al.,

1997), fast spiking interneurons and pyramidal cells both fire at

the oscillation frequency. Also, during persistent gamma activity

in CA3 (Fisahn et al., 1998) and neocortex (Buhl et al., 1998),

interneurons fire on every cycle or every other cycle; pyramidal

cells fire at much lower rates. Notably, our model demonstrated

that stable oscillations can nevertheless emerge from a network

with fast-firing PNs (Figures 6B–6D), a condition thought to be

unstable since excessive excitatory feedback from PNs to LNs

could potentially disrupt the rhythmic LN network.

The stability of the regime that we observed in the moth could

be explained by the combination of high-rate excitation and rela-

tively low-efficiency GABAA-mediated inhibition revealed by our


Neuron


recordings and our models. The overall weak inhibition that we

found in the moth AL (Figure S10) could also explain the relatively

weak dependency of the network oscillation frequency upon

the decay time constant of inhibition. Indeed, if fast,

GABAergic inhibition were strong enough to prevent excitatory

cells from firing, oscillatory frequency would depend strongly

on the time constant of inhibition (Whittington et al., 1995;

Buzsaki and Chrobak, 1995; Brunel and Wang, 2003; Bazhenov

et al., 2008), something we did not observe here (Figures S8B

and S8C). In moth, the net impact of inhibition seems restricted

to influencing the timing of spikes in excitatory neurons, thus

enabling periodic network rhythms. However, this inhibition

appears too weak to prevent excitatory cells from firing, enabling

them to maintain firing frequencies that exceed the network

oscillation frequency. The oscillatory regime revealed here may

be common, particularly in insects; unlike pyramidal cells, PNs

in the AL of honeybee (Stopfer et al., 1997), locust (Stopfer

et al., 2003), and Drosophila (Olsen et al., 2007) can respond to

stimuli with high firing rates.

EXPERIMENTAL PROCEDURES

Olfactory Stimulation

Odor stimulation was modified from Brown et al. (2005). Briefly, the odorized

headspace in 60 ml glass bottles above mineral-oil-diluted odorant solution

(10 ml) was pushed by a controlled volume of humidified air (0.1 l/min) into an

activated carbon-filtered, humidified air stream (0.75 l/min) flowingcontinuously

across the antenna. The longest stimulus we used (4 s) would deplete only about

13% of the vapor in the headspace, making it likely that each odor pulse varied

little in concentration throughout each stimulus. All chemicals were purchased

from Sigma-Aldrich (St. Louis, MO) unless otherwise noted. Odorants were

benzylalcohol, benzaldehyde, (+)-b-citronellene (Fluka Chemika, Buchs,

Switzerland), cyclohexanone, geraniol, hexanol, cis-3-hexenyl acetate,

(±)linalool (Aldrich Chemical Company Inc, Milwaukee, WI), methyl salicylate,

methyl jasmonate, 1-octanol (Fluka Chemika, Buchs, Switzerland), trans-2-

hexenal, trans-2-hexen-1-ol, oil extracts (strawberry, cinnamon, peach, lime,

jasmine [Balducci’s, Bethesda, MD]), thyme (Thyme Red, Saidel Inc., Renton,

WA), and wintergreen (Wagner’s). Odorant solutions were diluted (vol/vol) to

1% in mineral oil (J.T. Baker, Phillipsburg, NJ) unless otherwise noted.

Electrophysiology

Physiological data were obtained from 145 adult moths (Manduca sexta) of

both sexes reared from eggs (purchased from the NCSU Insectary, Raleigh,

NC) in our laboratory on an artificial diet (Bell and Joachim, 1976), under a

long-day photoperiod at 26�C and at more than 70% relative humidity. Adults

1 day posteclosion or older were dissected as described previously (Ito et al.,

2008). The head capsule was superfused with moth physiological saline

(Christensen and Hildebrand, 1987) at room temperature.

EAGs were recorded using Ag/AgCl wire (127 mm o.d.) inserted into the distal

tip of the antenna; the reference wire was inserted into the contralateral

compound eye. Signals were amplified with a DC amplifier (Model 440; Brown-

Lee Precision, San Jose, CA).

LFPs were recorded using saline-filled glass micropipettes with a long

shank (o.d. �3 mm, 4–10 MU), amplified, and low-pass filtered (>100 Hz)

by a DC amplifier (Brown-Lee Model 440). The long shank could be inserted

deep into the calyx of the MB where axons of PNs and the dendrites of

followers Kenyon cells make synaptic contacts. This technique allowed us to

record LFP oscillations more robust than those we could detect by the method

we use in locust (a blunt ended glass electrode with a short shank placed on

the cell body layer of the MB; see Brown et al., 2005).

Extracellular recordings of ORNs were made from sensilla in either isolated

antennae cut at their bases or intact antennae of restrained animals (both

methods yielded identical results). The antenna was stabilized with epoxy


carefully applied to leave the leading surface (where sensilla are located) acces-

sible. An electrochemically sharpened tungsten wire was inserted into the

sensillar base under a stereomicroscope (Leica MZ7.5). For isolated antenna

preparations, Ag/AgCl wires were placed in the cut ends. The proximal cut

end was immersed in a drop of saline or sensillum lymph (Kaissling, 1995),

which was covered with wax to prevent evaporation. For intact antenna prep-

arations, Ag/AgCl wires were placed in the distal end of the antenna and the

contralateral compound eye. Signals were amplified by a differential amplifier

(P55, GRASS Instruments; Telefactor, W. Warwick, RI) and sampled at 15

kHz (LabView software, PCI-MIO-16E-4 DAQ cards, National Instruments).

Intracellular recordings, subsequent fluorescent dye injection, histological

steps, and confocal imaging were made using sharp glass micropipettes as

described previously (Ito et al., 2008).

Full-Scale AL Network Model

The AL model included 820 PNs and 360 LNs (Homberg et al., 1989) simulated

using a reduced neuron model written in the form of difference equations (map;

Rulkov, 2002; Rulkov et al., 2004; Bazhenov et al., 2005; Rulkov and Bazhe-

nov, 2008). The time evolution of membrane voltage Vn was described as

nonlinear map Vn + 1 = faðVn; In + beIextn Þ; where In is a slow dynamical variable

describing the effects of slow conductances, fa is nonlinear function and n is

a discrete time step (�0.5 ms). The model’s properties and parameters are

shown in Figure S11. This model, despite its low intrinsic dimensionality,

produces a rich repertoire of dynamics and is able to mimic the dynamics of

Hodgkin-Huxley type neurons both at the single-cell level and in the context

of network dynamics (Rulkov et al., 2004; Bazhenov et al., 2005; Rulkov and

Bazhenov, 2008).

For synaptic connections, we used conventional first-order kinetic models

of fast synaptic conductances (Rulkov et al., 2004; Bazhenov et al., 2005)

(see Figure S11). All intrinsic connections (LN-LN, LN/PN, PN/LN) were

random with 0.5 probabilities. Maximal conductances (in dimensionless units;

see Rulkov et al., 2004) denoting the total excitation and inhibition received

by a given cell were set in most of the simulations to GACh(PN-LN) = 0.00015,

GGABA(LN-PN) = 0.00035, GGABA(LN-LN) = 0.00015.

The intensity (amplitude) of external (to mimic odor) stimuli to PNs and LNs

followed a Gaussian distribution truncated at 0.1 to avoid stimulating all PNs

(see Figure 7A). Which PNs and LNs received input with a particular intensity

was determined randomly. The proportion of LNs receiving non-zero input

was approximately one-third that of PNs receiving non-zero input. For

simplicity, we assumed that all ORNs (not only the best tuned ones) undergo

sensory adaptation. To mimic data obtained in vivo, the temporal variation

of the stimulus was approximated by the experimentally measured function

shown in Figure 5L.

Simplified Firing Rate Model

This simplified model contained 80 PNs and 30 LNs; qualitatively similar results

were obtained with a version of the model containing 800 PNs and 300 LNs. The

dynamics of each neuron in the network was modeled as a difference equation:

dvj

dt= � vjðtÞ

t+XN

k = 1

Wkj4ðvkðtÞÞ+ Ij

where vk is the firing rate of neuron k, t is the membrane time constant

of neuron (t = 10 ms), and f is a nonlinear logistic function

(4ðxÞ= ½1 + expð�a1,ðx � a2ÞÞ��1; a1 = 10, a2 = 0.6). Ij is the input from ORN

type j to PNj. LNs did not receive direct input from ORNs. The connectivity

matrix W included 50% connection probability: PN/LN (WPN_LN = 0.125)

and LN/PN (WLN_PN = �0.2). No PN/PN or LN/LN connections were

included. The integration step size (dt) was set to 1 ms. The model LFP was

computed by filtering summed PN activity (V). Since the number of PNs was

reduced in this model, LFP traces shown appear noisy.

Each ORN response was modeled after our physiological recordings. The

initial response from baseline to peak amplitude followed t,expð�t=triseÞ.Subsequently, ORN responses were reduced to reach an adapted state set

at 60% of the peak amplitude following expð�t=tadaptÞ. Finally, after the

odorant was removed, ORN responses returned back to baseline following

expð�t=tfallÞ. trise, tadapt, tfall for all 80 ORNs were set to 100 ms, 200 ms,

Neuron


and 250 ms, respectively. For any odor, 40% of PNs received non-zero ORN

input. Peak ORN response amplitude was uniformly, randomly distributed

between [0,1]. Model EAG responses (Figures 8G and 8I) were computed by

summing individual ORN firing-rate responses.

Data Analysis

All analyses except for spike sorting were performed using custom programs

in MATLAB (MathWorks Inc., Natick, MA). For experiments examining the

effect of odor pulse duration on oscillation frequency, ten pretrials (4 s) were

first delivered to elicit short-term ‘‘fast learning’’ response plasticity (Stopfer

and Laurent, 1999), and then 100, 250, 500, 750, 1000, 1500 ms duration

pulses were examined in a pseudorandom sequence; this set was repeated

three times in each animal. Spectrograms (500 ms sliding Hamming window

with 90% overlap) were normalized by the maximum value in the last pretrial.

Results from 18 trials each from three animals of either sex (each animal tested

with two odors) were averaged.

We used a magnitude squared coherence measure in Figure 1F to compare

LFPs recorded in the AL and the MB; this approach allowed us to minimize

the effect of small variations in phase we found in AL recordings caused by

differences in electrode placement. We calculated the magnitude squared

coherence using an overlapping sliding Hamming window (0.25 s with 80%

overlap) for fast (0.25–1 s) and slow (1–4 s) oscillations. For Figure 3B, which

did not require phase comparisons across brain structures, we used the

more standard cross-correlation measure.

We computed the phase of each spike relative to MB oscillations for fast

(0.3–0.8 s) and slow (0.8–4 s) oscillations as described elsewhere (Mazor

and Laurent, 2005) but modified as follows. LFP signals were acquired through

an analog low-pass filter (>100 Hz) of a DC amplifier (BrownLee Model 440),

which imposed a 7 ms delay, which we compensated for in MATLAB. For

the phase analysis, LFP signals were then digitally filtered (5–55 Hz, Butter-

worth; zero phase distortion by filtfilt command in MATLAB).

We measured the frequencies of LFP oscillations evoked by different

concentrations of three odors, each tested in blocks of ten trials that were

given in a randomized order. Power spectra were computed using the time

series in the first 0.5 s of odor responses as well as in the 1 s before the

odor responses (basal activity) and then averaged across ten trials. The oscil-

lation frequency was determined as the frequency with the maximum power in

14–54 Hz band in the average power spectrum.

Spike sorting of sensillum recordings was performed offline using Spike-o-

Matic software (Pouzat et al., 2002) implemented in Igor Pro (Wavemetrics,

Lake Oswego, OR). In ORNs, spike amplitude can change somewhat as

ORNs adapt to odors; to accommodate small changes in spike amplitude

we allowed each cell cluster to include events with varying amplitudes as

long as different sorted clusters remained well-separated (by at least five times

noise standard deviation), and, within a cluster, an appropriate interspike

interval distribution was maintained throughout an experiment. For the popu-

lation firing rate analysis shown in Figures 5D and 5E, in addition to well-sorted

units, we included unsorted data as multiunit activity from a single sensillum.

All other panels in Figure 5 include only well-sorted ORNs.

To fit the concentration responses of ORNs, we first counted the number of

spikes in the first 1 s of odor response (same analysis bin as F1 in Figure 5D)

and averaged over ten trials for each concentration. Similarly, the baseline

activity was measured from the 2 s just before the odor onset. ORN-odor

combinations not showing odor-elicited changes in spiking (<5 spikes/

response) were not included in this analysis.

SUPPLEMENTAL DATA

Supplemental Data can be found with this article online at http://www.cell.

com/neuron/supplemental/S0896-6273(09)00805-8.

ACKNOWLEDGMENTS

We are grateful to members of the Stopfer and Bazhenov laboratories for

helpful discussions and to Dr. Marit Stranden for sensilla lessons. We also

thank Dr. Kui Sun for her excellent animal care. Microscopy imaging was

performed at the Microscopy & Imaging Core (National Institute of Child Health

and Human Development, NIH) with the kind assistance of Dr. Vincent Schram.

This work was supported by the Japan Society for the Promotion of Science

(00169, 70510) to I.I., Joint NIH-NIST postdoctoral fellowship award by

National Research Council to B.R., grants from NIH-NIDCD and NIH-NINDS

to M.B. and an intramural grant from NIH-NICHD to M.S.

Accepted: October 6, 2009

Published: December 9, 2009

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Frequency Transitions in Odor-Evoked Neural Oscillations

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